Thermoplastic resin foamed articles, e.g., foamed articles of polyolefins, polyurethanes polyamides have been hitherto widely used as thermal insulation materials, cushioning materials and packaging materials. Such thermoplastic resin foamed articles are generally produced by a method in which cells are incorporated, a method in which a decomposed gas of a blowing agent is utilized, a solvent evaporation method or a method in which a gas is produced by a chemical reaction.
Meanwhile, an aromatic polyester, especially polyethylene terephthalate (hereinafter referred to as "PET") has been used in fibers, films, injection-molded articles, etc. because of its excellent mechanical properties, heat resistance, chemical resistance and dimensional stability. In recent years, there have been proposed a method in which these thermoplastic polyesters are foam-molded with various blowing agents (see Japanese Laid-open Patent Application (Kokai) No. 43,871/1977), and a method in which a uniform mixture of PET and polycarbonate or inorganic carbonate is heated at a temperature of 250.degree. to 350.degree. C. to react, and said heating temperature is maintained until CO.sub.2 is liberated, followed by foaming the reaction mixture (see Japanese Patent Publication No. 38,875/1972 and Japanese Laid-open Patent Application (Kokai) No. 41,966/1975). However, the former method involves defects such as coloration due to the blowing agent, foaming unevenness, decrease in mechanical properties. etc. The latter method possesses defects that the reaction has to be conducted at high temperatures for a long period of time and coloration of the reaction mixture and decrease in mechanical properties ace unavoidable. Further, a method for producing a foamed article by heat-melting PET containing a polyolefin and then incorporating an inert gas into the resin composition in the molten state (see Japanese Laid-open Patent Application (Kokai) No. 286,725/1990) has been also proposed. Said method using a crystalline PET, however, cannot give uniform fine cells and shows an foaming ratio of as low as less than 3.